An approach for determining the precise global geoid

Abstract

The task is to precisely determine the global geoid, which attracts a lot of geodesists' attention. Without precise knowledge of the density distribution in the domain between the geoid $\partial$G and the Earth's surface $\partial\Omega$­, it is almost impossible to complete the task. Under the assumption that the density distribution of the shallow mass layer bounded by $\partial\Omega$­ and a closed reference surface $\partial\Gamma$ that lies under the geoid $\partial$G is precisely given, an approach for completing the task is proposed. After the launch of the GOCE satellite system, it might be determined a precise global potential field V defined in the domain outside the Earth, and V is a regular harmonic field. The potential field $V_1$ generated by the shallow mass layer above $\partial\Gamma$ and defined in the domain outside $\partial\Gamma$ could be also determined, once the mass density distribution of the Earth's shallow mass layer is given. Then, with a technical procedure, it is theoretically determined the potential field (consequently the geopotential field W) generated by the Earth and defined in the domain outside $\partial\Gamma$. Finally, the geoid $\partialG$ is determined based on the basic equation W = $W_0$, where the constant $W_0$ is the value of the geopotential on the geoid, given by e.g. GRS80 system.